The present invention relates to an image display apparatus and, more particularly, to an image display apparatus reduced in overall size and weight, such as a head-mounted display apparatus which is retained on the user's head or face to project an image on the user's eyeball.
Helmet- and goggle-type image display apparatuses, which are designed to be retained on the user's head or face and hence called "head-mounted display apparatus" have heretofore been developed for the purpose of enabling the user to enjoy virtual reality or a wide-screen image by oneself.
There is a method of reducing the size of an optical system while maintaining favorable image forming characteristics by turning back the optical path using a half-mirror, as disclosed in Japanese Patent Application Laid-Open (KOKAI) No. 03-191389 (1991). U.S. Pat. No. 4,269,476 also discloses a similar technique.
FIG. 49 shows an optical system as one example of the above-described conventional technique. In the optical system, a half-mirror 2 is obliquely disposed in front of an observer's eye 1, and an image display device 3, e.g., a liquid crystal display device, and a magnifying reflecting mirror 4 are disposed to face each other across the half-mirror 2 and to extend parallel to the observer's line of sight. Let us consider the relationship between the vertical field angle of the optical system and the size of the half-mirror 2. As shown in FIG. 50, a straight line which passes through the center of the observer's pupil E when he or she observes the center of the field of view and which extends in the direction of the observer's line of sight at this time is defined as an x-axis. The point of projection on the x-axis of an end of the half-mirror 2 which is closer to the pupil E is defined as the origin of a coordinate system. Further, a direction, in which the distance from the x-axis to the half-mirror 2 increases as the distance from the pupil E increases within a plane defined by the x-axis and the line normal to the half-mirror 2 at the intersection of the x-axis and the half-mirror 2, is defined as a y-axis.
Assuming that the distance along the x-axis from the pupil E to the point of projection of the pupil-side end of the half-mirror 2 on the x-axis is d.sub.1, the length of the half-mirror 2 projected on the x-axis is d.sub.2, the diameter of the pupil E is epd, and the vertical field angle (half view angle) is 8, the following relationship holds: EQU epd/2+(d.sub.1 +d.sub.2)tan.theta.=d.sub.2 /2.times.tan45.degree.(1)
Hence, EQU d.sub.2 =(epd/2+d.sub.1 tan.theta.)/(1/2-tan.theta.) (2)
where tan.theta.&lt;1/2.
Since it is preferable to satisfy the conditions of epd.gtoreq.8 mm and d.sub.1 .gtoreq.20 mm, epd=8 mm and d.sub.1 =20 mm are substituted into Equation (2) as follows: EQU d.sub.2 =(4+20tan.theta.)/(1/2-tan.theta.) (3)
where tan.theta.&lt;1/2.
Under these conditions, when .theta.=10.degree., d.sub.2 =23.3 mm; when .theta.=15.degree., d.sub.2 =40.3 mm; and .theta.=20.degree., d.sub.2 =82.9 mm.
It is necessary in order to realize a compact optical system to satisfy the condition of .theta.&lt;15.degree.. Accordingly, the arrangement shown in FIG. 49 limits the achievement of a wide field angle.
Conventional methods of solving the above-described problem include one in which a beam splitter prism P is used to constitute a half-mirror, as shown in FIG. 51. This method will be explained below with reference to FIG. 52. The relationship between d.sub.2 and .theta. may be obtained in the same way as the above: EQU epd/2+d.sub.1 tan.theta.+d.sub.2 tan sin.sup.-1 sin.theta./n=d.sub.2 /2.times.tan45.degree. (4)
where n is the refractive index of the prism p.
Hence, EQU d.sub.2 =(epd/2+d.sub.1 tan.theta.) / (1/2-tan sin.sup.-1 sin.theta./n)(5)
where sin.theta.&lt;n.multidot.sin tan.sup.-1 1/2.apprxeq.0.447 n.
If epd=8 mm and d.sub.1 =20 mm are substituted into Equation (5) in the same way as the above, d.sub.2 is given by EQU d.sub.2 =(4+20tan.theta.)/(1/2-tan sin.sup.-1 sin.theta./n)(6)
Assuming that n=1.5, when .theta.=10.degree., d.sub.2 =19.6 mm; when .theta.=15.degree., d.sub.2 =28.8 mm; and when .theta.=20.degree., d.sub.2 =42.4 mm. Thus, the optical system becomes compact.
However, when .theta.=20.degree., the thickness of the prism P is 42.4 mm. Accordingly, the weight of the optical system increases by using the prism P, although the size of the optical system becomes small, that is, it is not greatly different from the size of an optical system which employs a half-mirror and in which .theta.=15.degree.. Therefore, it is demanded to make the optical system even more compact in the case of an optical system that uses a prism.
Incidentally, the above-mentioned Japanese Patent Application Laid-Open (KOKAI) No. 03-191389 (1991) discloses an arrangement which includes, as shown in the sectional view of FIG. 53, an image display device 3 for displaying the contents of information, a magnifying reflecting mirror 4 provided to face the image display device 3 so as to project the displayed contents on the observer's eyeball 1 as an enlarged image, and a half-mirror 2 disposed between the image display device 3 and the magnifying reflecting mirror 4, thereby enabling a wide-screen image to be obtained with a small-sized display apparatus. If the half-mirror 2 is provided with a function of transmitting an outside, real world image, light from the outside world also reaches the observer's eyeball 1, as shown by the broken line in the figure. Accordingly, the observer can see both an image displayed on the image display device 3 and an outside, real world image, which are superimposed on one another.
Even if the magnifying reflecting mirror 4 is a semitransparent mirror which is disposed opposite the eyeball, as shown in FIG. 54, advantages similar to those described above can be obtained.
There is also known an arrangement wherein the contents of information displayed on a display device are temporarily formed as an intermediate image by a relay optical system, and this image is projected on the observer's eyeball as an enlarged image by a magnifying reflecting mirror, as disclosed in U.S. Pat. No. 4,269,476.
Incidentally, the optical system of the above-described Japanese Patent Application Laid-Open (KOKAI) No. 03-191389 (1991) is a compact ocular optical system which is comprised of three parts in total, that is, an image display device, a half-mirror, and a surface reflecting mirror having a reflecting mirror directed toward the image display device, which serves as a magnifying reflecting mirror, as shown in FIGS. 53 and 54. However, Petzval sum PS, that is, EQU PS=.SIGMA.(1/nf)
which shows the flatness of the image surface, is inevitably smaller than 0, i.e., PS&lt;0, as a whole as long as the above-described arrangement is adopted because n=-1 and f&gt;0 in the case of a surface reflecting mirror. If the field angle is increased to obtain a wide-screen image by using an image display device of certain size, f decreases, and hence PS becomes a negative large value. Accordingly, the optical system of the conventional apparatus has the problem that the flatness of the image surface is impaired to a considerable extent. When the flatness of the image surface is inferior, there is a great difference between the center and edge of an image for observation in the position of an aerial enlarged image presented to the observer in the direction of the optical axis. Accordingly, the eye must have the accommodation function to work considerably, causing much fatigue to the observer's eye. Thus, the optical system is not suitable for a display apparatus. In addition, it becomes impossible to observe an image when projected closer to the eye than the near point of accommodation, which is the limit of the accommodation function of the eye.
As one example, FIGS. 55A-55I graphically show spherical aberration, astigmatism, distortion and coma in a case where the arrangement shown in FIG. 53 is adopted under the conditions that the radius r of curvature of the surface reflecting mirror is 54.3 mm, that is, the focal length f is 27.15 mm, and the field angle is 30.degree.. With regard to the amount of field curvature in this case, the difference between the center and edge of the observation image is equivalent to about 1 diopter. Accordingly, the amount of accommodation of the eye is considerably large. In this case, PS=1/(-1).times.27.15=-0.037.
In contrast to this, the optical system of U.S. Pat. No. 4,269,476 uses a relay optical system to temporarily form a curved intermediate image for the purpose of correcting such field curvature and projects an image of favorable flatness on the eyeball, with the intermediate image used as an object point, by using either a surface reflecting mirror or a reverse reflecting mirror. This optical system suffers, however, from the problem that the overall length of the ocular optical system is long and hence the overall size of the apparatus is large because of the use of a relay optical system. It is important for a head-mounted display apparatus to be small in the overall size with a view to enabling the user to feel comfortable when wearing the display apparatus, as a matter of course.